Question

Катер прошёл по течению 40 км и 6 км против течения , затратив на весь путь 3 часа. Какова собственная скорость катера , если скорость течения 2 км/ч.

Answer 1

пусть скорость катера х. скорость по течению х+2, протв течения х-2.Составляем уравнение

40/(х+2) + 6/(х-2)= 3

40(х-2)+6(х+2)-3(х+2)(х-2)=0

-3х^2 +46х -56=0

х1=14

х2=8/6(слишком маленькая для катера)

Значит ответ 14

Answer 2

Calculation of the Boat's Speed

To calculate the boat's speed, we can use the formula:

Boat's speed = Distance / Time

In this case, the boat traveled 40 km downstream (with the current) and 6 km upstream (against the current), taking a total of 3 hours for the entire journey. The speed of the current is given as 2 km/h.

Let's calculate the boat's speed:

1. Downstream speed: - Distance downstream = 40 km - Time taken downstream = x hours (to be determined) - Speed downstream = Distance downstream / Time taken downstream

2. Upstream speed: - Distance upstream = 6 km - Time taken upstream = 3 - x hours (since the total time is 3 hours and x hours were taken downstream) - Speed upstream = Distance upstream / Time taken upstream

3. Boat's speed: - Boat's speed = (Speed downstream + Speed upstream) / 2

Let's calculate the boat's speed using the given information:

1. Downstream speed: - Speed downstream = 40 km / x hours

2. Upstream speed: - Speed upstream = 6 km / (3 - x) hours

3. Boat's speed: - Boat's speed = (40 km / x hours + 6 km / (3 - x) hours) / 2

Now, let's solve this equation to find the value of x and then calculate the boat's speed.